Keys to Happiness? Parsing the Black Market’s Rate of Return

Readers may recall a piece I did back in April entitled Are Gold Chests Actually Worth it? The piece was a response to an apparent “leak” of information detailing the exact payouts and probabilities for the different event chests. I’d expected to find the house winning overall, and was pleasantly surprised to find that in fact, there was a positive expected value (EV).

Here’s a quick recap of what I wrote to explain the concept if you’re not already familiar, using an example of buying Magic: the Gathering cards:

…the idea behind EV is basically this: if the box of Magic costs $100, what is the value of the individual cards I’ll be opening? To derive that, you take market data on the value of all the possible cards (typically the rares and mythics, the cards that tend to have both the highest value and highest liquidity, and maybe uncommons). then factor that against the probability of getting each particular card in a box.

If the total EV was less than what you’d be spending on the box, then on the whole you’d be losing value. If it’s more, then you can expect a pretty good chance of coming out ahead. It’s worth noting that this is a guideline, not a flawless crystal ball. You could still luck out in a negative-EV set and get that “God-box” which happened to have all of the better rare cards, or some foil premium card, and come out well ahead. But then, you can’t judge success in a casino simply on that one time you win.

Today I noticed that Pixonic themselves had put out some official information on the Black Market on their site. It’s a far cry from what we had back in April, but it does offer some additional insight that we didn’t have before. I’d like to sift through it today and see if it offers us any guidance on the value of playing the Black Market.

As a personal disclaimer, my wife and I just welcomed our daughter Moira into the world. While I strive for accuracy, please forgive any computational errors as the product of a sleep-deprived mind.

As always with these sorts of promotions, your mileage may vary. You may have a lot of disposable income and don’t care about EV as long as you get one of the new Dash bots. Alternately, a new player may well find greater satisfaction than an established one because everything they win is something they may not have had already. So there’s your disclaimer- ultimately, the perception of worth and value is your own.

Right, so then what sort of data are we dealing with? Well, we don’t have a per-item breakdown with specific percentages for each, but Pixonic does at least provide us two things that we can evaluate which they note will go into effect for the 3.2 update. The first is the approximate value range of the prize categories.

Common: <= 20Au

Uncommon: 21-200Au

Rare: 201-1500Au

Epic: > 1500Au

Now, let’s start by assuming that as thrifty people who like to get the best deal, we all buy our Gold in $100 lots (ha!). That gives us a currency conversion of $1 USD = 140Au. On the opposite end of the scale, the $5 purchase is the least efficient, giving us an even $1 USD = 100Au. Since this is all napkin math, for convenience I’m going to split the difference and set the conversation at $1 USD = 120Au So how do those chests stack up now?

Common: <= $0.17 (a real penny arcade, this one)

Uncommon: Between $0.17 and $1.67

Rare: Between $1.67 and $12.50

Epic: Because this value range is open-ended, we’ll need to make some assumptions here. On the low end, this bracket starts at $12.50. The upper end would be a Dash bot, but as yet we have no way to really value them as no equivalencies have been established. I don’t think we’re building a bridge too far, however, to peg their value at $100. Recall that the Butch did have an established valuation at that price. Sure the Butch was a Heavy and these are Mediums, but those classifications are becoming less relevant.

So the epic, then, would be between $12.50 and $100.00. That’s a helluva variance, so let’s see if we can pin it down a bit more. Although we have no exact valuation of the Dash bots, we do know that the Superchests are epic-level-only loot. Perhaps we could look back at the last data we derived to find an average value? In our April analysis, there were fifteen different prize options in the Superchest, with an average value of 4,066Au. In other words, a rounded value of $34. We’ll go with that.

So now we’ve got a good idea of the value of outputs. What about the cost of inputs? I mean, you can grind Keys through gameplay, at which point winning anything other than the dreaded “less Keys” punch to the gut results in you coming out ahead to some degree.

Interestingly, Keys are pegged to the dollar just like Gold, but Pixonic isn’t quite so generous with the efficiency. $5 will get you 500Au or 500 Keys, but if you go for the bulk discount of $100 you get 14,000Au against only 13,000 Keys. Doing the same process as we did above, we arrive at a split-the-middle valuation of $1 USD = 115 Keys, and this allows us to put an approximate real-dollar pricetag on each chest.

Bronze: 10 Keys, or $0.09

Silver: 100 Keys, or $0.87

Gold: 1000 Keys, or $8.70

Super: We can’t really calculate this, as there’s no way to directly buy them. They’re free after opening enough chests, which I believe we estimated to be around 7.5 Gold chests. That makes them simply a value-add for a higher expenditure amount.

Now let’s tie everything together.

Fig. 1: Bronze Chest Payouts

So what does this tell us? Well, for one thing, while this might be the penny stocks of the War Robots world, the rate of return on investment is pretty decent. Almost 93% of the time you’re going to turn the nine cents of Keys into seventeen cents of value, and it only gets better from there.

By summing up the EV row, we end up with (rounded) $0.35. In EV terms, you’re nearly tripling your money. Again, this assumes all outcomes are of value to you. As I’ve mentioned before, if the Gareth you just won is the fourth Gareth you own, that might feel like a loss. The detailed tables we worked with back in April were so granular, we could actually calculate a precise EV tailored to what each person did and did not want. No such luxuries this time around.

But Jay, you say, what about the “less Keys” prize. Surely that’s a loss, right?

That’s sort of true, and also sort of misleading. You might spend 10 Keys to “win” 5 Keys, but being fair you did win something of value. It’s only when we compare it to the cost that it feels like a loss (which- also in fairness- it is). But since we’re dealing with a range of prizes for each category, these figures are approximate averages using the highest value range (as noted above).

Fig. 2: Silver Chest Payouts

How do Silver chests fare? Well, they cost around $0.87 per spin, with a total EV of $2.61. Again around triple the inlay. Thirty-nine cents of this is down to the 1.15% of an Epic prize, but even discounting that entirely you’re still ahead.

Fig. 3: Gold Chest Payouts

Now we’re talking real money, since it costs a little under nine bucks to open one of these things. And for that, what do you get? 17.22 in EV. Not quite as generous a rate as the previous two, but still a doubling of your purchase price.

This seems like a good time to issue a reminder that these are average returns, not guarantees. If you’re opening just one Gold chest, you might get the bogey prize of 500 Keys. Open, say, a hundred chests, and you’ll see the numbers bend to the average.

Open a bunch of chests, and you’ll get to throw one of these into the mix:

Fig. 4: Superchest Payouts

All gravy, baby! If you work towards one of these, your return on investment just went up. Even the “less Keys” bogey prize isn’t too bad here, with the minimum prize being 2,000 Keys- enough for two more Gold chests.

Takeaways

So again, we find that the rate of return of the Black Market– like the chests in the past Event- is skewed towards the players. You would think that this would lead to universal acclaim. Wait, you mean I can cash in this free stuff for even MORE free stuff? Bartender, I’ll have another!

But clearly this isn’t and hasn’t been the case. Why do we suppose that is? How could “free stuff” turn so many to the Dark Side? What is Pixonic doing wrong?

Feelbads

Let’s say there were two different carnival games available to play. Each of them cost a dollar. The game on the left doesn’t have huge prizes on its shelves, but you’re always going to get a prize that’s worth around a buck.

The other one, well, that’s not for the risk-averse. Most of the time you’re going to lose your money and get no prize. About 10% of the time, however, you’re going to win big- a nice, fat $10 prize.

Which game do you prefer?

There’s no wrong answer here, but the experience between the two couldn’t be more different. One of them hands out loads more feelbads to more folks, with just a fraction of the population getting the joy of hitting it big. The other isn’t ever going to produce those big-win moments, but you don’t have to worry about walking away empty-handed, either.

On the surface, the Black Market may seem to resemble the latter. After all, every spin is a winner, even if not every prize is equal. But I’d argue that the player experience clearly is mirroring the former.

After all, you spin the wheel and get some bullshit prize like 1Au or a “rebate” of half the Keys you used for the spin, you’re not feeling like a winner. You’re not feeling like you came anywhere near breaking even. Instead, you feel like a loser. That’s a hallmark of the higher-risk game. The safety net is illusory, and isn’t fooling anyone.

One thing Pixonic has to their advantage is that there are multiple levers available to them in the form of their different currencies. We’ve recently discussed the apparent pattern of the “soft retirement” of currencies, like Workshop Points (WSP) and (increasingly) even Gold. Thinking out loud, if Pixonic is already setting up a system where the player pool as a whole comes out ahead (+EV), they might consider implementing a system that reduces the feelbad awards at the balancing cost of a decreased chance for bigger wins.

Put another way, you’d skim off some of the happiness felt by the big winners… and redistribute it to all the losers.

“I like the sound of this plan already!”

The top-end winners won’t feel the loss of a few fractions of a percentage point, and besides, the big winners aren’t the one shaping the public narrative here. It’s all the losers in the public square lamenting how “greedy Pix” laughed all the way to the bank and all they got was this lousy tee-shirt with the picture of a Key on it.

Now, one of the purposes of these sorts of promotions is to act as a currency drain to prevent player stockpiling. This is why I’ve long maintained you’ll never see another WSP offer again, since so many players would simply open up their stale, bulging coffers of WSP rather than pay any real money for it. Instead, we’re seeing a complete reworking of the WSP system into “components.”

If drain is the name of the game, then this can be done by replacing losing prizes with parity conversion to less-desirable specie. Buying Keys for a dollar and winning fifty cents in Keys will always feel like a loss. But if instead you won a buck’s worth of WSP, well, that’s a less-valuable prize, but that loss is much better hidden.

Another main feelbad here is the cashing out system, where progress towards a Superchest is reset after every Black Market session. The reasons for this are both obvious and somewhat miserly, but there’s opportunity for innovation here as well.

What if each time you cashed out of a certain number of Keys at the end of a Market season, you got a “color mark” of that Key’s color. Get a “color mark” of each color, and you’d get to open some sort of “consolation prize” chest, not as good as a Superchest, but still free and fun, and takes some of the sting out of seeing your Superchest progress act out the labor of Sisyphus every few weeks.

And heck, it might even increase the incentive for repeat spending on different color cycles. It’s just a thought, but shows that resets don’t have to just feel like cash grabs.

Finally, we can’t overlook the concern in the community right now with Dash bots fueling some of the Black Market backlash. I’m not convinced that Pixonic has done everything it could have to take some of the sting away from the initial Dash distribution model. A lot of players seem blissfully unaware that this is a graduated release, assuming instead that the current model is the permanent model and reacting accordingly.

When Pixonic adjusts this in the future, as they stated from the outset in their Release Notes, these same folks may well choose to see this as “Pixonic being forced to react to outrage” instead of something that was pre-planned. More communication, transparency, and early release of information is how you mitigate a runaway narrative for the next time.

So in short, chests are pretty decent value, under the right circumstances and without guarantee. That said, this is always good advice:

11 comments on “Keys to Happiness? Parsing the Black Market’s Rate of Return”

Nice article. One note is that the above rates are for version 3.2, one can assume that the current version (3.1) has worse payouts. (Either because Pix is reacting to player frustration or because it is part of Pix’s poorly communicated opening up of accesses to the Dash bots via direct prizes and via components.) Since we don’t know the value of the equipment (components) that will drop in 3.2 perhaps you can revise this article after the component value is known?

Thanks for the article! I really appreciate the fact that you still keep us informed even while having a newborn baby to take care of.

I agree with most of the things that you have written, and seeing the superchest progress bar getting reset is definitively not pleasant at all. For those that aren’t buying chests, might as well make that bar invisible. Earning 7500 tokens in a single month is near impossible for casual players (I can’t even get halways to 1000 lol), so superchest is only really viable for those that are willing to drop in some credits. Of course, there just might be the crackshot that gets 4000 tokens from a bronze chest, but on the statistics, that seemed rather unrealistic.

My favorite chest to open is the silver chest, because that it’s affordable enough (I can’t play intensively), the prizes are okay and I’ve had a fondness towards it since that I found an apex sniper in it. Gold chest is usually the one that yields the best value prizes, but value dosn’t mean that it’s useful. I’ve still got 2 Gepards and 3 Gareths sitting around in the attic, twiddling their thumbs. (Do they have thumbs?)

I’m really unsure at this point exactly how much money Pixo expects the average player to have.

To trigger a Superchest you need at least 7,000 keys to start with, if not 8,000. You can’t earn that many, so that’s $80 upfront just to roll those dice. And the chests now have a lower chance of actually delivering something of real value, instead more likely to dish up component parts for something you already don’t have enough of, or gold that you can’t parlay back into another spin.